Solve the following equation for `x :` `"cos"(tan^(-1)x)=sin(cot^(-1)3/4)`, `tan(cos^(-1)x)=sin(cot^(-1)1/2)`

Answer

a) `x=frac{4}{5}`

b) `x=+-frac{sqrt5}{3}`

Explanation

A)We have,` cos (tan ^{-1} x)=sin (cot ^{-1} frac{3}{4})`


`Rightarrow cos (cos ^{-1} frac{1}{sqrt{x^{2}+1}})=sin (sin ^{-1} frac{4}{5})`


Let `tan ^{-1} {x}=theta_{1} Rightarrow tan theta_{1}=frac{{x}}{1}`


`Rightarrow cos theta_{1}=frac{1}{sqrt{x^{2}+1}} Rightarrow theta_{1}=cos ^{-1} frac{1}{sqrt{x^{2}+1}}`


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